Category

Systems of formal logic

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first-order logic

collection of formal systems used in mathematics, philosophy, linguistics, and computer science

study of type systems in mathematical logic and computer science

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intuitionistic logic

various systems of symbolic logic

theory of logic based on the orthocomplemented lattice of closed subspaces of a separable Hilbert space, regarded as the lattice of quantum propositions

paraconsistent logic

type of formal logic without explosion principle

second-order logic

extension of first-order logic allowing quantification over functions and relations

higher-order logic

form of predicate logic that is distinguished from first-order logic by additional quantifiers and, sometimes, stronger semantics

categorical logic

branch of category theory within mathematics, adjacent to mathematical logic but more notable for its connections to theoretical computer science.

infinitary logic

logic that allows infinitely long statements and/or infinitely long proofs

intermediate logic

propositional logic extending intuitionistic logic